1 Experiment #2: Telescopes And Microscopes Purpose: To ...

But from the similar triangles in this figure, we see that
hi =
ho i i
so that
o f ho f .
The angular magnification is defined as the increase in angular size,
m n
=
f .
Since a realistic lower limit on the focal length is a few centimeters in order to avoid getting
aberrations, simple magnifiers typically have magnifications no greater than 10.
The simple telescopes and microscope which you will build here are basically two-lens
optical systems, in which a converging lens (the objective) is used to form a real image of the
object, whether it be a tiny bug or a distant planet. A second lens called the eyepiece, which can
be either converging or diverging, is then used to examine the image formed by the objective.
In an astronomical (or Newtonian) telescope, the objective (“obj”) forms a real inverted
image I of a distant object O (such that o ) in its focal plane, as shown in Fig. 4 below. The
angular size of the image formed by the objective is given by
obj hi fobj where hi is the height of the image and fobj is the focal length of the objective. This is also the
angular size of the distant object, as we see in the following diagram.
h o
large distant
object
obj
h i'
inverted virtual
distant image
objective
obj
Fig. 4. Astronomical Telescope
The image I of the objective is the real object O' of height h o' = h i for the eyepiece, which is used
as a simple magnifier. The eyepiece then produces (as in Fig. 3) a virtual image I' which is
magnified in size to h i' but remains inverted. The angular size of the image seen through the
eyepiece (“eye”) is seen from Fig. 4 to be
eye h i
f eye
where f eye is the focal length of the eyepiece. The image I formed by the objective is very near the
focal point of the eyepiece, so that the distance L between the two lenses is approximately equal
to the sum of their focal lengths, L = f obj + f eye. The total angular magnification of the telescope is
M eye
obj
5
f obj
= f obj
f eye
f eye
eye
h i = h o'
eye
eyepiece
eye